Chatter Stability of Serrated Milling Tools in Frequency Domain

2021 ◽  
pp. 1-26
Author(s):  
Nima Dabiri Farahani ◽  
Yusuf Altintas
Keyword(s):  
Frequency Domain ◽  
Discrete Time ◽  
Time Domain ◽  
Angular Distance ◽  
Domain Model ◽  
Chatter Stability ◽  
Stability Diagrams ◽  
Time Marching ◽  
The Stability ◽  
Milling Tools

Abstract Serrated milling tools are widely used for chatter suppression in roughing difficult-to-cut Titanium and Nickel alloys in the aerospace industry. Due to the complexity of chip generation and serration wave geometries ground on the flutes, the chatter stability diagrams are predicted with time marching numerical simulation or semi-discrete time-domain methods, which are computationally too costly to use in practice. This paper presents a frequency domain model of milling dynamics with variable delays caused by the flute serrations. The endmill is divided into discrete cylindrical elements, each having a different radius from the cutter axis. As the cutter rotates and cuts metal, the angular distance between the subsequent tooth varies as a function of serration amplitudes and feedrate; hence the regenerative delays vary. The angular delays and effective directional factors are averaged for each tooth to form a time-independent but serration-dependent characteristics equation for all discrete cutter elements. The stability of the resulting characteristic equation of the system is solved using Nyquist theory and compared against the experimental results and existing time marching and semi-discrete time-domain solutions. The proposed analytical model predicts the stability charts about thirty times faster than the time-domain models while providing acceptable accuracy.

Chatter stability of milling in frequency and discrete time domain

2008 ◽  
Vol 1 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Y. Altintas ◽  
G. Stepan ◽  
D. Merdol ◽  
Z. Dombovari
Keyword(s):  
Discrete Time ◽  
Time Domain ◽  
Chatter Stability

Simulating High Mode Vortex Induced Vibration of Riser in Linear Sheared Current Using an Empirical Time Domain Model

2020 ◽  
Author(s):  
Sang Woo Kim ◽  
Svein Sævik ◽  
Jie Wu
Keyword(s):  
Frequency Domain ◽  
Vortex Shedding ◽  
Time Domain ◽  
Structural Model ◽  
Cross Flow ◽  
Domain Model ◽  
Vortex Induced Vibrations ◽  
The One ◽  
The Time Domain ◽  
Empirical Coefficients

Abstract This paper addresses the performance evaluation of an empirical time domain Vortex Induced Vibrations (VIV) model which has been developed for several years at NTNU. Unlike the frequency domain which is the existing VIV analysis method, the time domain model introduces new vortex shedding force terms to the well known Morison equation. The extra load terms are based on the relative velocity, a synchronization model and additional empirical coefficients that describe the hydrodynamic forces due to cross-flow (CF) and In-line (IL) vortex shedding. These hydrodynamic coefficients have been tuned to fit experimental data and by considering the results from the one of existing frequency domain VIV programs, VIVANA, which is widely used for industrial design. The feature of the time domain model is that it enables to include the structural non-linearity, such as variable tension, and time-varying flow. The robustness of the new model’s features has been validated by comparing the test results in previous researches. However, the riser used in experiments has a relatively small length/diameter (L/D) ratio. It implies that there is a need for more validation to make it applicable to real riser design. In this study, the time domain VIV model is applied to perform correlation studies against the Hanøytangen experiment data for the case of linear sheared current at a large L/D ratio. The main comparison has been made with respect to the maximum fatigue damage and dominating frequency for each test condition. The results show the time domain model showed reasonable accuracy with respect to the experimental and VIVANA. The discrepancy with regard to experiment results needs to be further studied with a non-linear structural model.

High Dimensional Harmonic Balance Analysis for Dynamic Piecewise Aeroelastic Systems

2008 ◽  
Author(s):  
Liping Liu ◽  
Earl H. Dowell
Keyword(s):  
Frequency Domain ◽  
Limit Cycle ◽  
Time Domain ◽  
Harmonic Balance ◽  
Solution Method ◽  
Computational Time ◽  
High Dimensional ◽  
Aeroelastic System ◽  
Time Marching ◽  
The Time Domain

This paper describes the extension and application of a novel solution method for the periodic nonlinear oscillations of an aeroelastic system. This solution method is a very attractive alternative to time marching algorithms in that it is much faster and may track unstable as well as stable limit cycles. The method is employed to analyze the nonlinear aeroelastic response of a two dimensional airfoil including a control surface with freeplay placed in an incompressible flow. The mathematical model for this piecewise aeroelastic system is initially formulated as a set of first order ordinary differential equations. A frequency domain solution for the limit cycle oscillations is derived by a novel high dimensional harmonic balance (HDHB) method. By an inverse Fourier transformation, the system in the frequency domain is then converted into the time domain. Finally, the airfoil motions are obtained by solving the system in the time domain for only one period of limit cycle oscillation. This process can be easily implemented into computer programs without going through the complex algebraic manipulations for the nonlinearities typical of a more conventional harmonic balance solution method. The solutions found using this new HDHB method have been shown to be the same as those found using a more traditional time marching (e.g. Runge-Kutta) approach and also a conventional harmonic balance approach in the frequency domain with a considerable computational time saving.

Vortex Induced Vibrations of Pipelines With Non-Linear Seabed Contact Properties

2016 ◽  
Author(s):  
Jan V. Ulveseter ◽  
Svein Sævik ◽  
Carl M. Larsen
Keyword(s):  
Frequency Domain ◽  
Linear Model ◽  
Time Domain ◽  
Structural Model ◽  
Life Time ◽  
Domain Model ◽  
Linear Interaction ◽  
Vortex Induced Vibrations ◽  
Non Linear ◽  
Soil Damping

A promising time domain model for calculation of cross-flow vortex induced vibrations (VIV) is under development at the Norwegian University of Science and Technology. Time domain, as oppose to frequency domain, makes it possible to include non-linearities in the structural model. Pipelines that rest on an irregular seabed will experience free spans. In these areas VIV is a concern with respect to the fatigue life. In this paper, a time domain model for calculation of VIV on free spanning pipelines is proposed. The model has non-linear interaction properties consisting of discrete soil dampers and soil springs turning on or off depending on the pipeline response. The non-linear model is compared to two linear models with linear stiffness and damping properties. One linear model is based on the promising time domain VIV model, while the other one is based on RIFLEX and VIVANA, which calculates VIV in frequency domain. Through four case studies the effect of seabed geometry, current velocity and varying soil damping and soil stiffness is investigated for a specific pipeline. The results show that there is good agreement between the results produced by VIVANA and the linear model. The non-linear model predicts smaller stresses at the pipe shoulders, which is positive for the life time estimations. Soil damping does not influence the response significantly.

Current spectrum estimation using Prony's estimator and coherent resampling

2014 ◽  
Vol 33 (3) ◽  
pp. 989-997 ◽  
Author(s):  
Michał Lewandowski ◽  
Janusz Walczak
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Domain Model ◽  
Spectrum Estimation ◽  
Nonlinear Load ◽  
Frequency Model ◽  
Content Type ◽  
Base Frequency ◽  
Current Spectrum

Purpose – A highly accurate method of current spectrum estimation of a nonlinear load is presented in this paper. Using the method makes it possible to evaluate the current injection frequency domain model of a nonlinear load from previously recorded time domain voltage and current waveforms. The paper aims to discuss these issues. Design/methodology/approach – The method incorporates the idea of coherent resampling (resampling synchronously with the base frequency of the signal) followed by the discrete Fourier transform (DFT) to obtain the frequency spectrum. When DFT is applied to a synchronously resampled signal, the spectrum is free of negative DFT effects (the spectrum leakage, for example). However, to resample the signal correctly it is necessary to know its base frequency with high accuracy. To estimate the base frequency, the first-order Prony's frequency estimator was used. Findings – It has been shown that the presented method may lead to superior results in comparison with window interpolated Fourier transform and time-domain quasi-synchronous sampling algorithms. Research limitations/implications – The method was designed for steady-state analysis in the frequency domain. The voltage and current waveforms across load terminals should be recorded simultaneously to allow correct voltage/current phase shift estimation. Practical implications – The proposed method can be used in case when the frequency domain model of a nonlinear load is desired and the voltage and current waveforms recorded across load terminals are available. The method leads to correct results even when the voltage/current sampling frequency has not been synchronized with the base frequency of the signal. It can be used for off-line frequency model estimation as well as in real-time DSP systems to restore coherent sampling of the analysed signals. Originality/value – The method proposed in the paper allows to estimate a nonlinear load frequency domain model from current and voltage waveforms with higher accuracy than other competitive methods, while at the same time its simplicity and computational efficiency is retained.

scholarly journals Study of Blockage Diagnosis for Hydrocyclone Using Vibration-Based Technique Based on Wavelet Denoising and Discrete-Time Fourier Transform Method

Processes ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 440 ◽  
Author(s):  
Guanghui Wang ◽  
Qun Liu ◽  
Chuanzhen Wang ◽  
Lulu Dong ◽  
Dan Dai ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Standard Deviation ◽  
Frequency Domain ◽  
Discrete Time ◽  
Time Domain ◽  
Wavelet Denoising ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Time Domain ◽  
Separation Devices

Hydrocyclones are extensively known as important separation devices which are used in many industrial fields. However, the general method to estimate device performance is time-consuming and has a high cost. The aim of this paper was to investigate the blockage diagnosis for a lab-scale hydrocyclone using a vibration-based technique based on wavelet denoising and the discrete-time Fourier transform method. The results indicate that the farther away the installation location from feed inlet the more regular the frequency is, which reveals that the installation plane near to the spigot generated the regular frequency distribution. Furthermore, the acceleration amplitude under blockage degrees 0%, 50% and 100% fluctuates as a sine shape with increasing time, meanwhile the vibration frequency of the hydrocyclone rises with increasing throughput. Moreover, the distribution of four dimensional and five non-dimensional parameters for the time domain shows that the standard deviation, compared to the others, reduced gradually with increases in blockage degree. Thus, the standard deviation was used to evaluate the online diagnosis of the blockage. The frequency domain distribution under different throughput reveals that the characteristic peaks consisting of the faulty frequency and multiple frequency were produced by the faulty blockage and the feed pump, respectively. Hence, the faulty peak of 16–17 Hz was adopted to judge the real-time blockage of the hydrocyclone, i.e., the presence of the characteristic peak marks the blockage, and its value is proportional to the blockage degree. The application of the online monitoring system demonstrates that the combination of the time domain and the frequency domain could admirably detect the running state and rapidly recognize blockage faults.

An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions and Large Depths of Cut

2001 ◽  
Author(s):  
Marc L. Campomanes ◽  
Yusuf Altintas
Keyword(s):  
Surface Finish ◽  
Time Domain ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Domain Model ◽  
Time Domain Simulation ◽  
Chatter Stability ◽  
Linear Effects ◽  
Deep Cuts ◽  
The Time Domain

Abstract This paper presents an improved time domain model for milling, which can simulate vibratory cutting conditions at very small radial widths of cut and large depths of cut. The improved kinematics model allows simulation of very small radial immersions. The varying dynamics modeled along the cutting depth allows milling with very flexible cutters and/or flexible workpieces at very deep cuts to be simulated. The model can predict forces, surface finish, and chatter stability, accurately accounting for non-linear effects that are difficult to model analytically. The discretized cutter and workpiece kinematics and dynamic models are used to represent the exact trochoidal motion of the cutter, and to investigate the effects of forced vibrations and changing radial immersion due to deflection and vibrations on chatter stability. Three dimensional surface finish profiles are predicted and are compared to measured results. Stability lobes generated from the time domain simulation are also shown for various cases.

Simulating Riser VIV in Current and Waves Using an Empirical Time Domain Model

2017 ◽  
Author(s):  
Mats J. Thorsen ◽  
Svein Sævik
Keyword(s):  
Frequency Domain ◽  
Vortex Shedding ◽  
Time Domain ◽  
Theoretical Background ◽  
Domain Model ◽  
Wave Period ◽  
Time Variability ◽  
Analysis Tool ◽  
Load Model ◽  
The Time Domain

The theoretical background of an empirical model for time domain simulation of VIV is reviewed. This model allows the surrounding flow to be time varying, which is in contrast to the traditional frequency domain tools. The hydrodynamic load model consists of Morison’s equation plus an additional term representing the oscillating effect of vortex shedding. The magnitude of the vortex shedding force is given by a dimensionless coefficient, and this force is assumed to act perpendicular to the relative velocity between the cylinder and the fluid. The time variability of the vortex shedding force is described by a synchronization model, which captures how the instantaneous frequency reacts to cylinder motion. The parameters in the time domain load model are calibrated against a commonly used frequency domain VIV analysis tool, VIVANA. To do this, a finite element model of a vertical tensioned riser is established, and the structure is exposed to a linearly sheared flow. Key results such as cross-flow displacements along the riser, frequency content, r.m.s. of bending stresses and mean in-line displacements are compared, and it is shown that the frequency and time domain methods are close to equivalent in this simple case with stationary flow. Finally, the time domain model is utilized to study VIV of a riser subjected to regular waves. The characteristics of wave induced VIV are discussed in light of the simulation results. It is seen that VIV is excited in the zone close to the surface, and the energy is transported downwards as traveling waves. The vibrations typically build up as the horizontal water particle velocity is high, and die out as the velocity decreases. The effect of varying the wave amplitude and period is investigated, and it is found that the dominating frequency, mode and r.m.s. stresses increase together with the wave height. The effect of the wave period is however more complicated. For example, reducing the wave period increases the dominating mode but decreases the displacements. Hence the stress may increase or decrease, depending on which of these effects are strongest.

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